Consider the repeated game in which the following stage game is played twice in succession, with payoffs averaged between the two rounds (and no discounting). d f 0,0 18, 18 48, 10 e а | 4у, 4y 10,0 b 0, 10 0,0 10, 48 40,40

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Jane is interested in buying a car from a used car dealer. Her maximum willingness to pay for thecar is 12 ($12,000). Bo, the dealer, is willing to sell the car as long as he receives at least 9($9,000). What is the Nash bargaining solution to this game?

In the normal form game below, the payoff matrix depends on the parameter a. 1 1 2 ABC a 0,2 6,4 -2,4 b 0, -24 -2a, 2a 8, 2 C 4,0 0,4 0, 14 Find the values of a, for which at least one pure strategy Nash equilibrium exists. Compute the value of a for which the expected payoff is the same for both players when the mixed strategy profile (01,02) = ((1/3,2/3,0), (0,1/4,3/4)) is played. Find the best response of player 1 (as a function of the parameter a) to player's 2 mixed strategy o2 = (1/2,1/2,0). Assuming a = 0 eliminate iteratively all dominated strategies and find a mixed strategy Nash equilibrium in this game.

Player 2 A B C А 2, 2 6,1 1,1 Player 1 B 1,6 5,5 1,1 1,1 1,1 4,4 Consider the simultaneous move game represented in normal form by this payoff matrix. Suppose that the game is repeated for two periods. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. (B, B) is played in the first period, (C, C) is played in the second period. (A, A) is played in both periods. (C, C) is played in both periods.

Determine all of the Nash equilibria (pure-strategy and mixed-strategy equilibria) of the following game: